This invention relates to methods and apparatus for testing gaseous flowmeters and, more particularly, it concerns an improved method and apparatus for eliminating accuracy errors caused by standing waves of sound encountered when testing gaseous flowmeters.
Public Utility Companies delivering natural gas to industrial complexes, factories, office buildings, hotels, apartments, hospitals, stores, homes, etc., are required to periodically verify the accuracy of the gas flowmeters used to bill the customers for the quantity of gas delivered.
Accuracy of the meters must be verified before being put in service and at specified intervals determined by the regulatory commissions of the states, cities, or local governmental authorities. A widely accepted method for testing is by the use of a portable transfer prover. This instrument system includes a very accurate "master meter" which is connected in series with the meter to be tested, so that a flow of air or natural gas may be transferred through both meters at various flow rates.
Portability of the proving system is important so that the transfer prover can be positioned near the installation site of the meter to be tested. Valves and fittings are normally provided so that the meter to be tested can be isolated from the gas line and a suitable pipe or flexible hose connection can be used to transfer the same gaseous flow through both meters in series. The volume readout of each meter can be compared after being corrected for temperature and pressure values of the flow through each meter. The accuracy determination is normally expressed as a percentage equivalent of the result indicated by the transfer prover master meter which has been calibrated to be 100% accurate at all flow rates.
The most accurate master meters are the positive displacement type. In this design the air or gas at the inlet of the meter is allowed to successively fill one cavity after another as they rotate to discharge each captured volume to the meter outlet. The cavities are rigid in shape and size, hence the name "positive displacement" meter.
A common form for this type of meter has two rotating impellers, each with two lobes which will produce four very small pulses in the air or gas stream for each complete revolution of the rotor assembly. Therefore, the frequency of the pulsations will be four times the revolutions per second of the meter impellers. When the displacement of the meter is known (cubic feet per revolution, CFR) and the flowrate is known (cubic feet per hour, CFH), the pulsation frequency can be easily determined: ##EQU1##
The impeller rotors in the positive displacement meters will appear at all times as a solid closure to a pressure wave-front travelling at the speed of sound in air or natural gas.
With reference to FIG. 1 of the drawings, if the inlet of a rotary positive displacement meter 10 is connected to a hose, tubing, or pipe 12 with the inlet to the tubing open to free space, the tube becomes a tuned one-quarter wavelength cavity. Such a cavity will resonate with sound waves at a fundamental frequency with a wavelength of four times the length of the cavity: ##EQU2## 1130 is the speed of sound in air, feet per second (or 1460 feet per second in natural gas)
L is the length of the cavity in feet PA0 F is the frequency of the sound wave (Hz) PA0 .DELTA. is the pipe open end correction which is equal to ##EQU3## D is the pipe diameter in feet PA0 L is the length of the cavity in feet PA0 F is the frequency of the sound wave (Hz) PA0 L is the length of the cavity in feet PA0 F is the frequency of the sound wave (Hz) PA0 .DELTA. is the pipe open end correction which is equal to ##EQU6## D is the pipe diameter in feet
When small pressure pulses occur at a rate which will resonate the cavity length, a standing wave sound will be sustained with a pressure node at the closed end and a velocity loop at the open end. This cavity will resonate only at "odd" harmonics of the fundamental frequency (3rd, 5th, 7th, etc.).
The true accuracy of the meter is not affected by these conditions, the problem lies in our inability to measure the true instantaneous pressure captured in each of the measuring chambers of the metering rotors. At or near resonant conditions, this pressure value will be different from the measured average flowing pressure which is normally used for pressure correction in test results. When the pressure correction is made with an incorrect pressure value, the accuracy of the test is also in error.
With reference to FIG. 2 of the drawings, if the inlet of a rotary positive displacement meter 14 is connected to a hose, tubing, or pipe 16 coupled to the outlet of another positive displacement meter 18, the tubing 16 is effectively closed at both ends for sound waves and becomes a tuned one-half wavelength cavity. Such a cavity will resonate with sound waves at a fundamental frequency with a wavelength of two times the length of the cavity: ##EQU4## 1130 is the speed of sound in air, feet per second (or 1460 feet per second in natural gas)
When the small pressure pulses occur at a rate which will resonate this cavity length, a standing wave of sound will be sustained with pressure nodes at both "closed" ends. This cavity will resonate at all harmonics of the fundamental (2nd, 3rd, 4th, 5th, 6th, etc.).
With reference to FIG. 3 of the drawings, if the inlet of a rotary positive displacement meter 20 is connected to a hose, tubing, or pipe 22 coupled to the outlet of a turbine meter 24, the tubing 22 is effectively closed to sound waves only at the positive displacement meter and is open through the turbine meter which is transparent to the sound waves at the velocity loop of the standing wave. Hence, the tubing 22 is closed at one end and open at the other and becomes a tuned one-quarter wavelength cavity. This cavity will resonate with sound waves at a fundamental frequency with a wavelength of four times the length of the cavity: ##EQU5## 1130 is the speed of sound in air, feet per second (or 1460 feet per second in natural gas)
The resonant harmonic frequencies will be only the 3rd, 5th, 7th, etc. odd harmonics of the calculated fundamental.
In order to reach typical meter locations conveniently, the length of the hose or tubing required to interconnect the prover master meter with the meter to be tested will be 20 or 30 feet. This range of cavity length, when excited by the wide range of pulsation frequencies of a positive displacement meter, will combine to pass through many harmonic resonant points over the range of flow rates to be used for testing meter accuracy. As such, when gaseous flowmeters are tested for determining the metering accuracy over the full range of flow rates, acoustic resonance at certain flow rates prevents accurate test results from portions of the range of flow rates which are necessary to validate the true measuring accuracy of the device.
Although an experienced and skilled technician can sometimes audibly sense flow rate regions where acoustic resonance may be a problem and select other flow rates by trial and error to locate flow rates not producing acoustic resonance, this is not only time-consuming but leads to a lower confidence factor for the overall accuracy of the test.
In light of the foregoing, there is a need for an improved method and apparatus for testing gaseous flowmeters.